Let up and Lay down

Let up verb - To come to an end.

Lay down and let up are semantically related In some cases you can replace term "Lay down" with "Let up", this phrasal verbs are similar.

Lay down verb - To put into effect through legislative or authoritative action.

Let up and lay down are semantically related in sleep topic. Sometimes you can use "Let up" instead a verb "Lay down".